The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced in [Benedetto et al, CMAME 2016] we are able to show an "almost uniform" error bound (in the sense that the unique term that depends in an unfavorable way on the parameters is damped by a higher order mesh-size multiplicative factor). We also introduce a novel discretization of the convection term that allows us to develop error estimates that are fully robust in the convection dominated cases. We finally present some numerical result.

翻译：这一贡献的目的是为在扩散-对流问题中SUPG稳定化的虚拟要素方法进行趋同分析,这种分析在对流主导制度中也很有力。对于[Benedetto等人,CMAME 2016]中最初采用的方法,我们能够显示一个“几乎一致”的误差(即在参数上以不利方式依赖的独特术语被更高顺序网格尺寸的多倍复制因子扭曲)。我们还采用了一种新的分解术语,使我们能够得出在对流主导情况下完全稳健的误差估计数。我们最后提出了一些数字结果。